Re: Tricky question, subspaces dimensions

Presumably, this question arose from the true statement that . When you try to extend this to 3 subspaces, you need to find , which is definitely not equal to . Basically, this is why Deveno's counter example above works. Notice though if or , then , and so in this case your original statement is true. (It boils down to the true statement about two subspaces.)

Re: Tricky question, subspaces dimensions

Originally Posted by johng

Presumably, this question arose from the true statement that . When you try to extend this to 3 subspaces, you need to find , which is definitely not equal to . Basically, this is why Deveno's counter example above works. Notice though if or , then , and so in this case your original statement is true. (It boils down to the true statement about two subspaces.)